Related papers: The phase transition in inhomogeneous random inter…

In this paper we study a version of (non-Markovian) first passage percolation on graphs, where the transmission time between two connected vertices is non-iid, but increases by a penalty factor polynomial in their expected degrees. Based on…

We study a point process describing the asymptotic behavior of sizes of the largest components of the random graph G(n,p) in the critical window p=n^{-1}+lambda n^{-4/3}. In particular, we show that this point process has a surprising…

We present an analytic formalism describing structural properties of random uncorrelated networks with arbitrary degree distributions. The formalism allows to calculate the main network characteristics like: the position of the phase…

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…

Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…

The following random graph model was introduced for the evolution of protein-protein interaction networks: Let $\mathcal G = (G_n)_{n=n_0, n_0+1,...}$ be a sequence of random graphs, where $G_n = (V_n, E_n)$ is a graph with $|V_n|=n$…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

We propose a random bipartite graph with weights assigned to both parts of the vertex sets. Edges are formed independently with probabilities that depend on these weights. This bipartite graph naturally gives rise to a random intersection…

When studying networks using random graph models, one is sometimes faced with situations where the notion of adjacency between nodes reflects multiple constraints. Traditional random graph models are insufficient to handle such situations.…

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…

Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…

We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…

We consider a recently introduced model of color-avoiding percolation defined as follows. Every edge in a graph $G$ is colored in some of $k\ge 2$ colors. Two vertices $u$ and $v$ in $G$ are said to be CA-connected if $u$ and $v$ may be…

We study the intersection of a random geometric graph with an Erd\H{o}s-R\'enyi graph. Specifically, we generate the random geometric graph $G(n, r)$ by choosing $n$ points uniformly at random from $D=[0, 1]^2$ and joining any two points…

We consider the Norros-Reittu random graph $NR_n(\textbf{w})$, where edges are present independently but edge probabilities are moderated by vertex weights, and use probabilistic arguments based on martingales to analyse the component sizes…

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…

We study a family of random permutation models on the Hamming graph $H(2,n)$ (i.e., the $2$-fold Cartesian product of complete graphs), containing the interchange process and the cycle-weighted interchange process with parameter $\theta >…

In this study we introduce and analyze the statistical structural properties of a model of growing networks which may be relevant to social networks. At each step a new node is added which selects 'k' possible partners from the existing…

As we add rigid bars between points in the plane, at what point is there a giant (linear-sized) rigid component, which can be rotated and translated, but which has no internal flexibility? If the points are generic, this depends only on the…

It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). Here we show that a…